(d) Using the formal - 6 definition of the limit, prove that x lim →∞ In x Hint: you may need to use the result of part (c) and the logarithm is an increasing function.
(d) Using the formal - 6 definition of the limit, prove that x lim →∞ In x Hint: you may need to use the result of part (c) and the logarithm is an increasing function.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
question d only
thank you
Transcribed Image Text:(d) Using the formal e - definition of the limit, prove that
lim
x→∞ ln x
Hint: you may need to use the result of part (c) and the logarithm is an increasing function.
![2. Here you will prove that lim
= ∞ without any use of L'Hopital's Rule.
→∞ In r
(a) For all positive integers n ≥ 1, prove that 2" > 2n.
(b) For all real numbers x ≥ 1, prove that 2r. Hint:Define n = [r].
(c) Recall e = 2.71828... is Euler's constant and e² is the exponential function. Since e > 2, you may
assume that lim ()* = ∞. Show that
et
lim == ∞0.
xx x
Hint: you may use the result of part (b) and a new Squeeze Theorem in one of the lectures.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4893c46-a94c-4c81-a9fc-277ce07300a6%2F25b36c23-248a-4f53-b6f1-14da896bc58e%2Fyx1wrrl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Here you will prove that lim
= ∞ without any use of L'Hopital's Rule.
→∞ In r
(a) For all positive integers n ≥ 1, prove that 2" > 2n.
(b) For all real numbers x ≥ 1, prove that 2r. Hint:Define n = [r].
(c) Recall e = 2.71828... is Euler's constant and e² is the exponential function. Since e > 2, you may
assume that lim ()* = ∞. Show that
et
lim == ∞0.
xx x
Hint: you may use the result of part (b) and a new Squeeze Theorem in one of the lectures.
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